Re: [ontolog-forum] PROF Swartz ON DEFINITIONS

[Alex Shkotin <alex.shkotin@xxxxxxxxx>]

Hi Rich,

It seems that in FOL we do not have a definition at all:

suppose we have binary predicate R (primary or defined) and we introduce new predicate R_ and two axioms with it:

"R(x,y) hence R_(x,y)"

and

"R_(x,z) and R(z,y) hence R_(x,y)"

We can't say that we have definition for R_ as we need to add "the smallest..." as for transitive closure (http://en.wikipedia.org/wiki/Transitive_closure).

What do you think?

Alex

2010/9/18 Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx>

Ferenc,

 

How about

 

If     _x is an ancestor of _z

And _z is the father of _y

Or   _z is the mother of _y

Then _x is an ancestor of _y.  

 

The basis relations include:

_ is the father of _

_ is the mother of _

 

And the term defined with recursion, is

_ is an ancestor of _

 

Each expansion of the Horne clause during the query must be instantiated with some variable or constant in order to continue expanding the search backward.  If at any point, the database runs out of father and mother facts, then recursion stops.  But that fact doesn’t show up in FOL as clearly as in the software function that interprets it, and which must specifically figure out how to stop the recursion when there is no more fodder for the query.  

 

-Rich

 

Sincerely,

Rich Cooper

EnglishLogicKernel.com

Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

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From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of FERENC KOVACS
Sent: Saturday, September 18, 2010 8:17 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: [ontolog-forum] PROF Swartz ON DEFINITIONS

 

IN THE SAME DOCUMENT

Recursive Definitions
(Advanced material) By a "direct ancestor" we mean one's "parents, grandparents, great-grandparents, etc." More formally, we might write:

"x is a direct ancestor of y" =_df "x is a parent of y; or x is a parent of a parent of y; or x is a parent of a parent of a parent of y; etc."

 

My comments: is it not the referent that the definition is about?C ompare with the statement in the front above: quote

 

For example, the term, "pain", is defined, but pain itself is not defined. We define only terms, never their referents. end of quote

 

Ferenc

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